*THE POPULAR SCIENCE MONTHLY*

required to drive the feed water pump), and the quantity of heat is delivered to the condenser.

According to the first law of thermodynamics, the work must be equal to , both quantities of heat being expressed in energy units. Therefore

(9) |

As far as the net result is concerned the operation of the steam engine may be thought of as (a) the conversion into work of the whole of the heat H_{1} from temperature T_{1}, and (*b*) the reconversion of a

portion of this work into heat at temperature . The regeneration^{[1]} associated with process (*a*) is equal to according to equation (8), and the degeneration associated with process (*b*) is equal to according to equation (8). If the operation of the engine involves sweeping processes, then the degeneration must exceed the regeneration , that is, we must have

style="text-align:center;"| | (10) |

or, substituting the value of from equation (9) and solving for , we have

(11) |

The fractional part of the heat which is converted into work by the engine is called the efficiency of the engine, and the inequality (11) shows that the efficiency of any engine working between temperatures and must be less than whatever the nature of the working fluid and whatever the design of the engine.

*The Perfect Engine.*—An engine involving no irreversible or sweep-

- ↑ To convert an amount of work into heat at a given temperature involves an amount of degeneration, and to convert the heat into work involves the same amount of what may be called thermodynamic regeneration.